Q: What are the factor combinations of the number 32,254,321?

 A:
Positive:   1 x 3225432111 x 293221117 x 1897313137 x 235433187 x 1724831259 x 256191507 x 214032329 x 13849
Negative: -1 x -32254321-11 x -2932211-17 x -1897313-137 x -235433-187 x -172483-1259 x -25619-1507 x -21403-2329 x -13849


How do I find the factor combinations of the number 32,254,321?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 32,254,321, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 32,254,321
-1 -32,254,321

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 32,254,321.

Example:
1 x 32,254,321 = 32,254,321
and
-1 x -32,254,321 = 32,254,321
Notice both answers equal 32,254,321

With that explanation out of the way, let's continue. Next, we take the number 32,254,321 and divide it by 2:

32,254,321 ÷ 2 = 16,127,160.5

If the quotient is a whole number, then 2 and 16,127,160.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 32,254,321
-1 -32,254,321

Now, we try dividing 32,254,321 by 3:

32,254,321 ÷ 3 = 10,751,440.3333

If the quotient is a whole number, then 3 and 10,751,440.3333 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 32,254,321
-1 -32,254,321

Let's try dividing by 4:

32,254,321 ÷ 4 = 8,063,580.25

If the quotient is a whole number, then 4 and 8,063,580.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 32,254,321
-1 32,254,321
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

111171371871,2591,5072,32913,84921,40325,619172,483235,4331,897,3132,932,21132,254,321
-1-11-17-137-187-1,259-1,507-2,329-13,849-21,403-25,619-172,483-235,433-1,897,313-2,932,211-32,254,321

More Examples

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